Since space science is a strong subject of mine, I'll try and explain the difference between a Meteor and an Asteroid as best I can:
Asteroids come from a belt of rocks (from the size of dust up to the size of dwarf planets) between the orbits of Mars and Jupiter. These rocks are left over debris from the formation of the planets. These rocks become known as Meteoroids once they enter Earth's atmosphere and only become known as Meteorites once they hit ground and even then, it's only if they survive the impact.
Very complicated system to people who don't know it.
Now, I can hear some people asking: "Well what the hell is a Comet then!?"
Well, whereas Asteroids are objects made of mostly rock and metal, Comets are a mix of rock and water ice (which causes the tail when they stray too close to the Sun). Also, whereas Asteroids tend to come from the belt between Mars and Jupiter, all Comets come from the "Kuiper belt", which is another belt of rocks left over from the formation of the planets. This one being beyond the orbit of Neptune. The former planet and current Dwarf planet Pluto is a large member of this belt.
EDIT to mention: Some Comets also come from Oort cloud, which is even further out from the Sun than the Kuiper belt.
Isn't it simple when you know!